Accumulated Other Comprehensive Loss - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	$ 928,504	$ 874,756	$ 958,474	$ 839,779
Total other comprehensive (loss) income, net of tax	(1,303)	841	(3,516)	116
Ending balance	928,438	904,649	928,438	904,649
Foreign Currency Translation Adjustments
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(36,925)	(32,724)	(34,679)	(31,609)
Other comprehensive (loss) income before reclassifications	(1,361)	722	(3,607)	(393)
Income tax (expense) benefit	0	0	0	0
Other comprehensive (loss) income before reclassifications, net of tax	(1,361)	722	(3,607)	(393)
Amounts reclassified from accumulated other comprehensive loss	0	0	0	0
Income tax benefit	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	0	0	0	0
Total other comprehensive (loss) income, net of tax	(1,361)	722	(3,607)	(393)
Ending balance	(38,286)	(32,002)	(38,286)	(32,002)
Pension Obligations, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(2,377)	(2,555)	(2,410)	(2,945)
Other comprehensive (loss) income before reclassifications	0	0	(34)	451
Income tax (expense) benefit	0	0	8	(101)
Other comprehensive (loss) income before reclassifications, net of tax	0	0	(26)	350
Amounts reclassified from accumulated other comprehensive loss	75	154	151	205
Income tax benefit	(17)	(35)	(34)	(46)
Amounts reclassified from accumulated other comprehensive loss, net of tax	58	119	117	159
Total other comprehensive (loss) income, net of tax	58	119	91	509
Ending balance	(2,319)	(2,436)	(2,319)	(2,436)
Accumulated Other Comprehensive Loss
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(39,302)	(35,279)	(37,089)	(34,554)
Other comprehensive (loss) income before reclassifications	(1,361)	722	(3,641)	58
Income tax (expense) benefit		0	8	(101)
Other comprehensive (loss) income before reclassifications, net of tax	(1,361)	722	(3,633)	(43)
Amounts reclassified from accumulated other comprehensive loss	75	154	151	205
Income tax benefit	(17)	(35)	(34)	(46)
Amounts reclassified from accumulated other comprehensive loss, net of tax	58	119	117	159
Total other comprehensive (loss) income, net of tax	(1,303)	841	(3,516)	116
Ending balance	$ (40,605)	$ (34,438)	$ (40,605)	$ (34,438)